M
Math Coach Amy
Amy Ferguson Moncure

H Algebra 2/Trig · Unit 4

Direct, Inverse, or Joint

Decide whether an equation is direct variation, inverse variation, or joint variation.

Jump to section:

Key Ideas Easy Medium Hard

Direct: y = kx.

Inverse: y = kx.

Joint: y = kxz.

What to Remember

Direct

Direct variation has the form y = kx.

y = kx² is still direct. It varies directly with the square of x.

Inverse

Inverse variation has the form y = kx, or xy = k.

y = kx² varies inversely with the square of x.

Joint

Joint variation uses two or more variables multiplied.

y = kxz varies jointly with x and z.

The constant

k is the constant of variation.

You do not need the value of k to name the variation.

Level 1

Easy

y = kx or y = kx

Example
Name the variation. y = 7x

The form is y = kx.

y = 7x

This equation matches that form.

Direct variation.

Answer: direct variation

1
Name the variation. xy = 8
Show Answer

The form is xy = k.

xy = 8

This equation matches that form.

Inverse variation.

Answer: inverse variation

2
Name the variation. y = 9x
Show Answer

The form is y = kx.

y = 9x

This equation matches that form.

Direct variation.

Answer: direct variation

3
Name the variation. y = 4x
Show Answer

The form is y = kx.

y = 4x

This equation matches that form.

Inverse variation.

Answer: inverse variation

4
Name the variation. y = 15x
Show Answer

The form is y = kx.

y = 15x

This equation matches that form.

Direct variation.

Answer: direct variation

5
Name the variation. xy = 6
Show Answer

The form is xy = k.

xy = 6

This equation matches that form.

Inverse variation.

Answer: inverse variation

Level 2

Medium

A square or a square root

Example
Name the variation. y = 5x²

The form is y = kx².

y = 5x²

This equation matches that form.

Direct variation.

Answer: direct variation

1
Name the variation. y = 8x²
Show Answer

The form is y = kx².

y = 8x²

This equation matches that form.

Inverse variation.

Answer: inverse variation

2
Name the variation. y = 3×square root of x
Show Answer

The form is y = k×square root of x.

y = 3×square root of x

This equation matches that form.

Direct variation.

Answer: direct variation

3
Name the variation. y = 6square root of x
Show Answer

The form is y = ksquare root of x.

y = 6square root of x

This equation matches that form.

Inverse variation.

Answer: inverse variation

4
Name the variation. y = 4x²
Show Answer

The form is y = kx².

y = 4x²

This equation matches that form.

Direct variation.

Answer: direct variation

5
Name the variation. y = 9x²
Show Answer

The form is y = kx².

y = 9x²

This equation matches that form.

Inverse variation.

Answer: inverse variation

Level 3

Hard

Two or more variables multiplied

Example
Name the variation. y = 3xz

The form is y = kxz.

y = 3xz

This equation matches that form.

Joint variation.

Answer: joint variation

1
Name the variation. z = 4xy
Show Answer

The form is z = kxy.

z = 4xy

This equation matches that form.

Joint variation.

Answer: joint variation

2
Name the variation. A = 6bh
Show Answer

The form is A = kbh.

A = 6bh

This equation matches that form.

Joint variation.

Answer: joint variation

3
Name the variation. y = 2xw
Show Answer

The form is y = kxw.

y = 2xw

This equation matches that form.

Joint variation.

Answer: joint variation

4
Name the variation. V = lwh
Show Answer

The form is V = klwh.

V = lwh

This equation matches that form.

Joint variation.

Answer: joint variation

5
Name the variation. y = 5x×square root of z
Show Answer

The form is y = kx×square root of z.

y = 5x×square root of z

This equation matches that form.

Joint variation.

Answer: joint variation

Need help naming variation?

Book a Session with Amy